Type IIB supergravity solutions for polarized IKKT

Abstract

The general local solutions to complexified Type IIB supergravity which are invariant under the complex Lie superalgebra $F(4)$, and which were derived and classified in arXiv:2508.14959, are supplemented here by the construction of their flux potentials and field strengths. We then focus on the Type IIB$^\star$ real form of complex Type IIB supergravity, where we obtain solutions with spacetime metric of the warped product form $dS_{1,5}\times S^2\timesΣ$. We systematically derive boundary and regularity conditions under which the $dS_{1,5}\times S^2\timesΣ$ solutions can be analytically continued to regular $S^6\times S^2\timesΣ$ solutions in Euclidean Type IIB supergravity. Using these results, we construct explicit global solutions. These solutions include explicit realizations of recent proposals for a holographic description of the polarized IKKT model, and we clarify the charges carried by these solutions. We also obtain novel solutions in the same regularity class with different brane charges.